Learning Guide for Algebra for College Students

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to his Developmental Algebra Series, Bob has written textbooks covering college algebra, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson Education. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

• 1. Algebra, Mathematical Models, and Problem Solving1.1 Algebraic Expressions, Real Numbers, and Interval Notation1.2 Operations with Real Numbers and Simplifying Algebraic Expressions1.3 Graphing Equations1.4 Solving Linear EquationsMid-Chapter Check Point Section 1.1—Section 1.41.5 Problem Solving and Using Formulas1.6 Properties of Integral Exponents1.7 Scientific NotationChapter 1 Group ProjectChapter 1 SummaryChapter 1 Review ExercisesChapter 1 Test2. Functions and Linear Functions 2.1 Introduction to Functions2.2 Graphs of Functions2.3 The Algebra of FunctionsMid-Chapter Check Point Section 2.1—Section 2.32.4 Linear Functions and Slope2.5 The Point-Slope Form of the Equation of a LineChapter 2 Group ProjectChapter 2 SummaryChapter 2 Review ExercisesChapter 2 TestCumulative Review Exercises (Chapters 1—2)3. Systems of Linear Equations3.1 Systems of Linear Equations in Two Variables3.2 Problem Solving and Business Applications Using Systems of Equations3.3 Systems of Linear Equations in Three VariablesMid-Chapter Check Point Section 3.1—Section 3.33.4 Matrix Solutions to Linear Systems3.5 Determinants and Cramer's RuleChapter 3 Group ProjectChapter 3 SummaryChapter 3 Review ExercisesChapter 3 TestCumulative Review Exercises (Chapters 1—3)4. Inequalities and Problem Solving4.1 Solving Linear Inequalities4.2 Compound Inequalities4.3 Equations and Inequalities Involving Absolute ValueMid-Chapter Check Point Section 4.1—Section 4.34.4 Linear Inequalities in Two Variables4.5 Linear ProgrammingChapter 4 Group ProjectChapter 4 SummaryChapter 4 Review ExercisesChapter 4 TestCumulative Review Exercises (Chapters 1—4)5. Polynomials, Polynomial Functions, and Factoring5.1 Introduction to Polynomials and Polynomial Functions5.2 Multiplication of Polynomials5.3 Greatest Common Factors and Factoring By Grouping5.4 Factoring TrinomialsMid-Chapter Check Point Section 5.1—Section 5.45.5 Factoring Special Forms5.6 A General Factoring Strategy5.7 Polynomial Equations and Their ApplicationsChapter 5 Group ProjectChapter 5 SummaryChapter 5 Review ExercisesChapter 5 TestCumulative Review Exercises (Chapters 1—5)6. Rational Expressions, Functions, and Equations 6.1 Rational Expressions and Functions: Multiplying and Dividing6.2 Adding and Subtracting Rational Expressions6.3 Complex Rational Expressions6.4 Division of PolynomialsMid-Chapter Check Point Section 6.1—Section 6.46.5 Synthetic Division and the Remainder Theorem6.6 Rational Equations6.7 Formulas and Applications of Rational Equations6.8 Modeling Using VariationChapter 6 Group ProjectChapter 6 SummaryChapter 6 Review ExercisesChapter 6 TestCumulative Review Exercises (Chapters 1—6)7. Radicals, Radical Functions, and Rational Exponents 7.1 Radical Expressions and Functions7.2 Rational Exponents7.3 Multiplying and Simplifying Radical Expressions7.4 Adding, Subtracting, and Dividing Radical ExpressionsMid-Chapter Check Point Section 7.1—Section 7.47.5 Multiplying with More Than One Term and Rationalizing Denominators7.6 Radical Equations7.7 Complex NumbersChapter 7 Group ProjectChapter 7 SummaryChapter 7 Review ExercisesChapter 7 TestCumulative Review Exercises (Chapters 1—7)8. Quadratic Equations and Functions 8.1 The Square Root Property and Completing the Square8.2 The Quadratic Formula8.3 Quadratic Functions and Their GraphsMid-Chapter Check Point Section 8.1—Section 8.38.4 Equations Quadratic in Form8.5 Polynomial and Rational InequalitiesChapter 8 Group ProjectChapter 8 SummaryChapter 8 Review ExercisesChapter 8 TestCumulative Review Exercises (Chapters 1—8)9. Exponential and Logarithmic Functions 9.1 Exponential Functions9.2 Composite and Inverse Functions9.3 Logarithmic Functions9.4 Properties of LogarithmsMid-Chapter Check Point Section 9.1—Section 9.49.5 Exponential and Logarithmic Equations9.6 Exponential Growth and Decay; Modeling DataChapter 9 Group ProjectChapter 9 SummaryChapter 9 Review ExercisesChapter 9 TestCumulative Review Exercises (Chapters 1—9)10. Conic Sections and Systems of Nonlinear Equations10.1 Distance and Midpoint Formulas; Circles10.2 The Ellipse10.3 The HyperbolaMid-Chapter Check Point Section 10.1—Section 10.310.4 The Parabola; Identifying Conic Sections10.5 Systems of Nonlinear Equations in Two VariablesChapter 10 Group ProjectChapter 10 SummaryChapter 10 Review ExercisesChapter 10 TestCumulative Review Exercises (Chapters 1—10)11. More on Polynomial and Rational Functions11.1 Polynomial Functions and Their Graphs11.2 Zeros of Polynomial FunctionsMid-Chapter Check Point Section 11.1—Section 11.211.3 Rational Functions and Their GraphsChapter 11 Group ProjectChapter 11 SummaryChapter 11 Review ExercisesChapter 11 TestCumulative Review Exercises (Chapters 1—11)12. Sequences, Induction, and Probability12.1 Sequences and Summation Notation12.2 Arithmetic Sequences12.3 Geometric Sequences and SeriesMid-Chapter Check Point Section 12.1—Section 12.312.4 The Binomial Theorem12.5 Mathematical Induction12.6 Counting Principles, Permutations, and Combinations12.7 ProbabilityChapter 12 Group ProjectChapter 12 SummaryChapter 12 Review ExercisesChapter 12 TestCumulative Review Exercises (Chapters 1—12)AppendixWhere Did That Come From? Selected Proofs